Hello,
It is widely known how to express the density of states in terms of the retarded Green function, rho(E) = Im(trace (G(E, x,x))), etc.
Can anyone suggest please a reference where the same quantity is obtained via functional methods of Quantum Field Theory? (in terms of, say functional derivatives of partition funtion, or Feynman diagrams)
Many thanks
Dear Luiz,
The question is not which fromalizm to use to calculate the trace - the standard (feymnam) one, or the one you call Schrodinger. The question is how the density is DEFINED in fucntional terms and why so?
Dear Ignat, I would suggest to start thinking from the point of view of physical STM measurement. Consider coupling the field theory to fermionic quantum mechanics at one point x. H_QM = E_0 \psi^\dag \psi . This quantum mechanics have only one energy level E_0. Now couple this QM to field theory with known constant matrix element. We know that tunneling amplitude must be related to local DOS. On the other hand, this tunneling amplitude is a physical observable, so, it may be written as an observable in any correct functional formulation
Dear Sergey,
I stay on purely theoretical grounds and cannot think in terms of STM or any other measurement =(
My starting point is a partition function (as a path integral or even already integrated, whatever) Z[j,J,..] of some relativistic QFT model including several fields with corresponding external currents j, J,...
The question now is how to define for some/all of the them the density of states?